Mathnificent Word of the Week

Tdorante10, CC BY-SA 4.0, via Wikimedia Commons

substitution

/sǝb-stǝ-’tü-shǝn/

noun

A strategy for solving systems of equations that include solving for one variable and using that solution to find the other variable.

"It became common practice that Reggie would consider making a substitution at the halfway point of the process, for the betterment of the entire project."

Tdorante10, CC BY-SA 4.0, via Wikimedia Commons

I’m wondering if it’s time to move around the support players
in order to simplify the flow of the entire game.

Allrighty. We’re ten weeks into the new year, how’s 2023 going for ya?

Though I’m pretty self-reliant, I absolutely need the support of my peers to reach my goals for expanding the audience of Kate Loves Math*. We gotta keep on lifting each other up, right?

Now, I’m a fool for baseball and a couple of weeks ago Major League Baseball spring training began. Spring Training is like a dress rehearsal; everyone’s in uniform and they’re going through the entire 9 innings and they are playing to win, but each team is also moving players around and testing them in different positions and changing up batting orders with a lot more frequency than they do during the regular season. And there seems to be a pitcher substitution almost every inning.

Which got me thinking about the past 9 weeks (oooh, like 9 innings

) and whether it might be a good idea to just, you know, evaluate my own (support) team and – if needed – apply the mathematical process of solving by substitution .

Here's a mathematical example of solving by substitution:
You have two equations to solve where 'x' and 'y' are each representing a number.
                          x = 2y - 4      and     2x = 3y - 5
Since the value of x and y are the same for both equations, if you can figure out what number x represents in one equation then you can substitute that same number for x in the other equation. This should help in figuring out the corresponding y value and solving both equations.

Quite simply, I’m reassessing what I knew about my peers in the beginning of the year based on recent conversations. There’s definitely some people (let’s call them ‘x’) who have additional knowledge and skills that I didn’t know – 9 weeks ago – that they possessed. So, I’m wondering if I can substitute the specific skills someone has to support me in reaching one goal for another goal that I hadn’t even considered they’d be able to support me with.

And that all made me wonder if you might want to try this solve by substitution process yourself. Sometimes while working a plan there is new information about a key element that’s casually served up, yours for the taking – and for the re-positioning. Lemme know if you run through some scenarios of your own and if this analytic process helps you – and your team – better accomplish what you’re going for.

For those who actually read those equations above >>>